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Output Feedback Invariants
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TLDR
In this article, it was shown that there exists a quasi-projective variety whose points parameterize the output feedback orbits in a unique way, and that in the closure of every feedback orbit there is exactly one nondegenerate system.Abstract:
The paper is concerned with the problem of determining a complete set of invariants for output feedback. Using tools from geometric invariant theory it is shown that there exists a quasi-projective variety whose points parameterize the output feedback orbits in a unique way. If the McMillan degree $n\geq mp$, the product of number of inputs and number of outputs, then it is shown that in the closure of every feedback orbit there is exactly one nondegenerate system.read more
Citations
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Journal ArticleDOI
New solution method of linear static output feedback design problem for linear control systems
TL;DR: A new method of construction of the linear static output feedback for linear control systems is offered, which consists in construction of an initial approximation of the feedback matrix such that a numerical sequence converges to an exact solution to the feedback design problem.
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Bruhat canonical form for linear systems
W. Manthey,Uwe Helmke +1 more
TL;DR: In this paper, a new canonical form for state space equivalence of controllable and observable linear systems is introduced, which is closely related to a canonical form due to Bosgra and van der Weiden.
Journal Article
Mismatching Problem between Generic Pole-assignabilities by Static Output Feedback and Dynamic Output Feedback in Linear Systems
TL;DR: It is proved that the minimum d-th order dynamic output feedback compensator for pole-assignment in m-input, p-output, n- fourth order systems is quantitatively decomposed into static output feedback compensated and its associated d number of arbitrary 1st order dynamic elements in augmented (m-d)-input, (p+d)-output, (n+D)-th order systems.
Journal ArticleDOI
Full static output feedback equivalence
TL;DR: In this article, a constructive solution to the problem of full output feedback equivalence, of linear, minimal, time-invariant systems, is presented, where the equivalence relation on the set of systems is transformed to another on a set of invertible block Bezout/Hankel matrices using the isotropy subgroups of the full state feedback group and the full output injection group.
References
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Book
Geometric Invariant Theory
TL;DR: Geometric invariant theory for moduli spaces has been studied extensively in the mathematical community as mentioned in this paper, with a large number of applications to the moduli space construction problem, see, for instance, the work of Mumford and Fogarty.
Journal ArticleDOI
Moduli of representations of the fundamental group of a smooth projective variety I
TL;DR: In this article, the authors present a legal opinion on the applicability of commercial or impression systématiques in the context of the agreement of publication mathématique de l'I.H.S.
Journal ArticleDOI
Structural Invariants of Linear Multivariable Systems
TL;DR: In this article, the structural properties of the matrix triple (C,A,B) which remain invariant under various transformation groups are identified, and a brief account of a recent result which states that the controllable space of a matrix triple can be decomposed into a direct sum of singly-generated controllability subspaces, the dimension of each subspace being determined by one of the controLLability indices of
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Invariants and Canonical Forms under Dynamic Compensation
William A. Wolovich,Peter Falb +1 more
TL;DR: In this article, a complete abstract invariant and a set of canonical forms under dynamic compensation for linear systems characterized by proper, rational transfer matrices are presented. But the complexity of the problem is not addressed.
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